Suppose we are interested in the impact of advertisement on sales for a given go

Question

Suppose we are interested in the impact of advertisement on sales for a given good. We have data for a cross-section of n firms, thus i = 1, ...., n. We believe that the correct specification of the model is

Si = ?1 + ?2Ai + ?Si (3) Ai = ?1 + ?2Si + ?Ai , (4)

where A and S indicate expenditure on advertisement and total sales, respec- tively. ?Si and ?Si are disturbance terms with zero mean and Cov(?Si , ?Ai ) = 0.

(i) Derive the reduced form equations for S and A.

(ii) Give a mathematical explanation of what are the consequences of estimat-

ing the parameters of (3) by OLS.

(iii) Examine the identification status of each equation.

Now suppose that the true model is
Si = ?1 + ?2Ai + ?Si (5)

Ai = ?1 + ?2Si + ?3SZi + ?Ai , (6)

where SZi denotes the size of firm i. SZ can be considered exogenous.

(iv) Examine the identification status of equations (5) and (6).

(v) How would you consistently estimate the parameters in (5)?

Explanation / Answer

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